Pyrochlore/defect fluorite zirconates

ABSTRACT

A composition comprising a rare earth-doped zirconium/hafnium oxide is provided that has a defect-fluorite structure or a pyrochlore structure. The rare earth-doped zirconium/hafnium oxide has a formula: (Ln1aLn2aLn3aLn4aLn5b)2M2O7 where each of Ln1, Ln2, Ln3, Ln4, and Ln5 is a different rare earth element such that Ln1 and M have a first atomic radius ratio that is 1.35 to 1.45, Ln2 and M have a second atomic radius ratio that is 1.35 to 1.45, Ln3 and M have a third atomic radius ratio that is 1.46 to 1.78, and Ln4 and M have a fourth radius ratio that is 1.46 to 1.78; a is 0.2 or 0.25; b is 0.2 when a is 0.2, and b is 0 when a is 0.25; and M is Zr, Hf, or a mixture thereof. Methods of forming a coating that includes this composition, along with the resulting coated components, are also provided.

PRIORITY INFORMATION

The present application claims priority to Indian Provisional PatentApplication No. 202211008138 filed on Feb. 16, 2022.

FIELD OF TECHNOLOGY

This disclosure broadly relates to ultra-low thermal conductivitypyrochlore/defect fluorite zirconates. More particularly, thisdisclosure generally relates to compositions suitable for use in coatingsystems on components exposed to high-temperature environments, such asthe hot gas flow path through a gas turbine engine.

BACKGROUND

The use of thermal barrier coatings on components such as combustors,high pressure turbine (HPT) blades and vanes of gas turbine engines isincreasing. Generally, the thermal insulation of a TBC enables suchcomponents to survive higher operating temperatures, increases componentdurability, and improves engine reliability. In order for a TBC toremain effective throughout the planned life cycle of the component itprotects, it is desired that the TBC has a low thermal conductivitythroughout the life of the component, including high temperatureexcursions. Additionally, it is desired that the TBC has a hightoughness which reduces the damage due to erosion and impact on rotatingcomponents of HPTs, combustor components, and static turbine components(e.g., turbine nozzles). Low thermal conductivity TBCs can increaseefficiency by reducing heat loss and potentially allowing highertemperature operation.

Current TBC material 8YSZ is known for its high toughness, but also highthermal conductivity. Low thermal conductivity compositions such as55YSZ lacks high toughness. Thus, further improvements in TBC technologyare desirable, particularly as TBCs are employed to thermally insulatecomponents intended for more demanding engine designs.

BRIEF DESCRIPTION OF THE DRAWINGS

A full and enabling disclosure of the present disclosure, including thebest mode thereof, directed to one of ordinary skill in the art, is setforth in the specification, which makes reference to the appended Figs.,in which:

FIG. 1 is a cross-sectional side view of an exemplary coated component;and

FIG. 2 is a schematic cross-sectional view of an exemplary gas turbineengine according to various embodiments of the present subject matter.

Repeat use of reference characters in the present specification anddrawings is intended to represent the same or analogous features orelements of the present disclosure.

Definitions

As used herein, the word “exemplary” means “serving as an example,instance, or illustration.” Any implementation described herein as“exemplary” is not necessarily to be construed as preferred oradvantageous over other implementations. Additionally, unlessspecifically identified otherwise, all embodiments described hereinshould be considered exemplary.

The term “gas turbine engine” refers to an engine having a turbomachineas all or a portion of its power source. Example gas turbine enginesinclude turbofan engines, turboprop engines, turbojet engines,turboshaft engines, etc., as well as hybrid-electric versions of one ormore of these engines. The term “turbomachine” or “turbomachinery”refers to a machine including one or more compressors, a heat generatingsection (e.g., a combustion section), and one or more turbines thattogether generate a torque output.

In the present disclosure, when a layer is being described as “on” or“over” another layer or substrate, it is to be understood that thelayers can either be directly contacting each other or have anotherlayer or feature between the layers, unless expressly stated to thecontrary. Thus, these terms are simply describing the relative positionof the layers to each other and do not necessarily mean “on top of”since the relative position above or below depends upon the orientationof the device to the viewer.

Chemical elements are discussed in the present disclosure using theircommon chemical abbreviation, such as commonly found on a periodic tableof elements. For example, hydrogen is represented by its common chemicalabbreviation H; helium is represented by its common chemicalabbreviation He; and so forth.

As used herein, “Ln” refers to a rare earth element or a mixture of rareearth elements. More specifically, the “Ln” refers to the rare earthelements of scandium (Sc), yttrium (Y), lanthanum (La), cerium (Ce),praseodymium (Pr), neodymium (Nd), promethium (Pm), samarium (Sm),europium (Eu), gadolinium (Gd), terbium (Tb), dysprosium (Dy), holmium(Ho), erbium (Er), thulium (Tm), ytterbium (Yb), lutetium (Lu), ormixtures thereof.

As used herein, the term “substantially free” is understood to meancompletely free of said constituent, or inclusive of trace amounts ofsame. “Trace amounts” are those quantitative levels of chemicalconstituent that are barely detectable and provide no benefit to thefunctional or aesthetic properties of the subject composition. The term“substantially free” also encompasses completely free.

As used herein, the term “substantially equal” is understood to beinclusive of a minor trace variation of a quantitative level that isbarely detectable and provides no benefit to the functional or aestheticproperties of the subject composition. The term “substantially equal”also encompasses completely equal.

DETAILED DESCRIPTION OF PARTICULAR EMBODIMENTS

Reference now will be made in detail to embodiments of the disclosure,one or more examples of which are illustrated in the drawings. Eachexample is provided by way of explanation of the disclosure, notlimitation of the disclosure. In fact, it will be apparent to thoseskilled in the art that various modifications and variations can be madein the present disclosure without departing from the scope of thedisclosure. For instance, features illustrated or described as part ofone embodiment can be used with another embodiment to yield a stillfurther embodiment. Thus, it is intended that the present disclosurecovers such modifications and variations as come within the scope of theappended claims and their equivalents.

Compositions are generally disclosed that are based on a rareearth-zirconium/hafnium oxides having a pyrochlore or defect-fluoritestructure, along with coatings formed with such compositions. Thesecompositions and coating may have a relatively low thermal conductivity(e.g., 0.5 W/m-K to 1.5 W/m-K at 1000° C., such as 0.5 W/m-K to 1.4W/m-K at 1000° C., in a 95-100% dense puck as measured via a laser flashmethod according to ASTM E1461-13). Generally, these compositions may beused to form a layer of a TBC that has an ultra-low thermalconductivity, along with suitable toughness (e.g., an indentationfracture toughness of 2 MPa-m^(0.5) to 3 MPa-m^(0.5) in a 95-100% densepuck).

In one particular embodiment, the layer of the TBC may have a singlephase (i.e., either a pyrochlore structure or defect-fluoritestructure). Thus, the resulting TBC would allow for higher componentsurface temperatures and/or reduced coating thickness for the samesurface temperature. Reduced TBC thickness, especially in applicationslike combustors which require relatively thick TBCs, would result in asignificant cost reduction as well as weight benefit.

The composition generally includes a rare earth-doped zirconium/hafniumoxide having a defect-fluorite structure or a pyrochlore structure. Inone embodiment, the rare earth-doped zirconium/hafnium oxide has aformula as shown in Formula 1:

(Ln¹ _(a)Ln² _(a)Ln³ _(a)Ln⁴ _(a)Ln⁵ _(b))₂M₂O₇  Formula 1:

where each of Ln¹, Ln², Ln³, Ln⁴, and Ln⁵ is a different rare earthelement such that Ln¹ and M have a first atomic radius ratio that is1.35 to 1.45, Ln² and M have a second atomic radius ratio that is 1.35to 1.45, Ln³ and M have a third atomic radius ratio that is 1.46 to1.78, and Ln⁴ and M have a fourth radius ratio that is 1.46 to 1.78; ais 0.2 or 0.25; b is 0.2 when a is 0.2, and b is 0 when a is 0.25; and Mis Zr, Hf, or a mixture thereof.

Generally, each of Ln¹ and Ln² is a different rare earth element thatforms a defect fluorite as Ln₂Zr₂O₇ (e.g., Tb, Dy, Y, Ho, Er, Tm, Yb,and Lu) and/or forms a defect fluorite as Ln₂Hf₂O₇ (e.g., Dy, Y, Ho, Er,Tm, Yb, and Lu). In particular embodiments, each of Ln¹ and Ln² is adifferent rare earth element selected from the group consisting of Tb,Dy, Y, Ho, Er, Tm, Yb, and Lu.

Alternatively, each of Ln³ and Ln⁴ is a different rare earth elementthat forms a pyrochlore as Ln₂Zr₂O₇ (e.g., La, Ce, Pr, Nd, Pm, Sm, Eu,and Gd) and/or forms a pyrochlore as Ln₂Hf₂O₇ (e.g., La, Ce, Pr, Nd, Pm,Sm, Eu, Gd, and Tb). In particular embodiments, each of Ln¹ and Ln² is adifferent rare earth element selected from the group consisting of La,Ce, Pr, Nd, Pm, Sm, Eu, Gd, and Tb.

In one particular embodiment, a is 0.2 such that the rare earth-dopedzirconium/hafnium oxide has a formula as shown in Formula 2:

(Ln¹ _(0.2)Ln² _(0.2)Ln³ _(0.2)Ln⁴ _(0.2)Ln⁵ _(0.2))₂M₂O₇  Formula 2:

where each of Ln¹, Ln², Ln³, Ln⁴, and Ln⁵ is a different rare earthelement such that Ln¹ and M have a first atomic radius ratio that is1.35 to 1.45, Ln² and M have a second atomic radius ratio that is 1.35to 1.45, Ln³ and M have a third atomic radius ratio that is 1.46 to1.78, and Ln⁴ and M have a fourth radius ratio that is 1.46 to 1.78; andM is Zr, Hf, or a mixture thereof. In such an embodiment, Ln⁵ and M mayhave a second atomic radius ratio that is either 1.35 to 1.45 or 1.46 to1.78.

In another particular embodiment, a is 0.25 and b is 0 such that therare earth-doped zirconium/hafnium oxide has a formula as shown inFormula 3:

(Ln¹ _(0.25)Ln² _(0.25)Ln³ _(0.25)Ln⁴ _(0.25))₂M₂O₇  Formula 3:

where each of Ln¹, Ln², Ln³, and Ln⁴ is a different rare earth elementsuch that Ln¹ and M have a first atomic radius ratio that is 1.35 to1.45, Ln² and M have a second atomic radius ratio that is 1.35 to 1.45,Ln³ and M have a third atomic radius ratio that is 1.46 to 1.78, and Ln⁴and M have a fourth radius ratio that is 1.46 to 1.78; and M is Zr, Hf,or a mixture thereof.

As stated, M in any of Formulas 1, 2, or 3 may be Zr, Hf, or a mixturethereof due to the similarity of ZrO₂ and HfO₂ chemistries and the ionicradii of Zr⁴⁺ (0.72 Å) and Hf⁴⁺ (0.71 Å). Thus, M may be 0 atomic % to100 atomic % of Zr. Conversely, M may be 0 at. % to 100 at. % of Hf.However, in particular embodiments, Zr may form half or more of theatomic percentage of M, such that M is 50 atomic % to 100 atomic % ofZr. In one particular embodiment, Zr is the predominate constituent of M(e.g., M is 95 atomic % to 100 atomic % of Zr). For instance, in certainembodiments, M may consist of Zr (i.e., M is 100 atomic % of Zr).

Particularly suitable compositions of rare earth-doped zirconium/hafniumoxide having a defect-fluorite structure or a pyrochlore structure mayinclude, but are not limited to:

(Nd_(0.2)Eu_(0.2)Y_(0.2)Dy_(0.2)Lu_(0.2))₂Zr₂O₇;(Nd_(0.2)Eu_(0.2)Tb_(0.2)Dy_(0.2)Lu_(0.2))₂Zr₂O₇;(Sm_(0.2)Eu_(0.2)Gd_(0.2)Dy_(0.2)Lu_(0.2))₂Zr₂O₇;(Sm_(0.2)Eu_(0.2)Y_(0.2)Dy_(0.2)Lu_(0.2))₂Zr₂O₇;(Nd_(0.2)Eu_(0.2)La_(0.2)Dy_(0.2)Lu_(0.2))₂Zr₂O₇;(Nd_(0.2)Eu_(0.2)Ho_(0.2)Dy_(0.2)Lu_(0.2))₂Zr₂O₇;(Nd_(0.2)Eu_(0.2)Y_(0.2)Dy_(0.2)Er_(0.2))₂Zr₂O₇;(Nd_(0.2)Eu_(0.2)Ho_(0.2)Dy_(0.2)Er_(0.2))₂Zr₂O₇;(Sm_(0.2)Eu_(0.2)Ho_(0.2)Dy_(0.2)Lu_(0.2))₂Zr₂O₇;(Nd_(0.25)Eu_(0.25)Ho_(0.25)Dy_(0.25))₂Zr₂O₇;(Nd_(0.25)Eu_(0.25)Y_(0.25)Dy_(0.25))₂Zr₂O₇;(Sm_(0.25)Eu_(0.25)Ho_(0.25)Dy_(0.25))₂Zr₂O₇; or mixtures thereof.

As stated above, the compositions of rare earth-doped zirconium/hafniumoxide having a defect-fluorite structure or a pyrochlore structure areparticularly suitable for use in a layer of a thermal barrier coating ona component.

Referring to FIG. 1 , for example, an exemplary coated component 100 isshown formed from a substrate 102 having a surface 103 with a coatingsystem 106 thereon. Generally, the coating system 106 includes a bondcoat 104 on the surface 103 of the substrate 102, and a TBC 108 on thebond coat 104. In the embodiment shown, the bond coat 104 is directly onthe surface 103 without any layer in between. Bond coat materials widelyused in TBC systems may include, but are not limited to,oxidation-resistant overlay coatings such as MCrAlX (where M is iron,cobalt and/or nickel, and X is yttrium or another rare earth element),and oxidation-resistant diffusion coatings such as diffusion aluminidesthat contain aluminum intermetallics.

The substrate 102 may be any suitable material, for example a metal suchas steel or superalloys (e.g., nickel-based superalloys, cobalt-basedsuperalloys, or iron-based superalloys, such as Rene N5, N500, N4, N2,IN718, Hastelloy X, or Haynes 188) or other suitable materials forwithstanding high temperatures. The coating system 106 may be disposedalong one or more portions of the substrate 102 or disposedsubstantially over the whole exterior of the substrate 102. Inparticular embodiments, the coating system 106 may have a totalthickness of 50 micrometer (e.g., micron or μm) to 2500 μm, such as 100μm to 700 μm.

The TBC 108 may be formed from a plurality of individual layers 114. Inone embodiment, at least one of the layers 114 of the TBC 108 includes alayer comprising the composition of rare earth-doped zirconium/hafniumoxide having a defect-fluorite structure or a pyrochlore structure (suchas having the formula of Formula 1). For example, at least one of thelayers 114 of the TBC 108 may include at least 80% by weight of thecomposition of rare earth-doped zirconium/hafnium oxide having adefect-fluorite structure or a pyrochlore structure (such as having theformula of Formula 1). In one embodiment, at least one of the layers 114of the TBC 108 may include 90% by weight to 100% by weight of thecomposition of rare earth-doped zirconium/hafnium oxide having adefect-fluorite structure or a pyrochlore structure (such as having theformula of Formula 1).

In particular embodiments, each of the layers 114 of the TBC 108 mayhave a layer thickness of 25 μm to 100 μm (e.g., 25 μm to 50 μm).

One or more of the individual layers 114 may be formed from a stabilizedceramic that can sustain a fairly high temperature gradient such thatthe coated metallic components can be operated at gas temperatureshigher than the metal's melting point. For instance, the stabilizedceramic material may be one or more of yttria stabilized zirconia (YSZ)and other rare-earth-stabilized zirconia compositions, mullite(3Al₂O₃-2SiO₂), alumina, ceria (CeO₂), lanthanum rare-earth zirconates,rare-earth oxides (e.g., La₂O₃, Nb₂O₅, Pr₂O₃, CeO₂), and metal-glasscomposites, and combinations thereof (e.g., alumina and YSZ or ceria andYSZ). Besides its high temperature stability, YSZ also has a goodcombination of high toughness and chemical inertness, and the thermalexpansion coefficient of YSZ is a comparatively suitable match to thatof the metallic components being coated.

The individual layers 114 may be formed by any suitable process. Forinstance, one or more individual layer 114 may be formed by air-plasmaspray (APS), suspension plasma spray (SPS), solution precursor plasmaspray (SPPS), electron beam physical vapor deposition (EBPVD), highvelocity oxygen fuel (HVOF), electrostatic spray assisted vapordeposition (ESAVD), and direct vapor deposition.

In one embodiment, the TBC 108 may include a layer based on an YSZ(e.g., 8YSZ) closest to the substrate 102, such as directly on the bondcoat 104 (if present). As such, the yttria-stabilized zirconia may forma barrier coating positioned between the substrate and the layercomprising the composition of rare earth-doped zirconium/hafnium oxidehaving a defect-fluorite structure or a pyrochlore structure (such ashaving the formula of Formula 1).

The coated component 100 is particularly suitable for use as a componentfound in high temperature environments, such as those present in gasturbine engines, for example, combustor components, turbine blades,shrouds, nozzles, heat shields, and vanes. In particular, the coatedcomponent 100 may be a component positioned within a hot gas flow pathof the gas turbine such that the coating system 106 forms a thermalbarrier for the underlying substrate 102 to protect the component 100within the gas turbine when exposed to the hot gas flow path.

The coating including the rare earth-doped zirconium/hafnium oxide maybe achieved by making use of powder feedstock synthesized fromwet-chemical synthesis routes using suitable metal (Ln, Hf, Zr)precursors, either organic (e.g., alkoxides such propoxide, butoxide,isopropoxide, ethoxide, tetraethoxide, or triethoxide of metal) orinorganic (e.g., chlorides, oxychlorides, nitrates, oxynitrates,carbonates of metal), in a suitable solvent (e.g., aqueous or organic orcombination). Suitable organic solvents may include, but are not limitedto, isopropanol, ethanol, butanol, or ethylene glycol monobutyl ether.Additional components in the wet chemical route may include an organicacid (e.g., citric acid or acetic acid), an inorganic acid (e.g., HCl orHNO₃), an organic base (e.g., diethylamine, triethylamine, ordiethylenetriamine), or an inorganic base (e.g., NaOH or NH₄OH).Viscosity modifiers (e.g., glycerol, ethylene glycol, ethylacetate, orpolyethylene glycol) may also be present. Non-limiting examples ofwet-chemical routes include sol-gel, polymer precursor orgel-combustion, hydrothermal or solvothermal, co-precipitation,co-precipitation hydrothermal combination, and co-precipitation moltensalt method combination. In these methods, the initial processing may becarried out at room-temperature to about 200° C., after which aheat-treatment at low temperatures of 500° C. to 1000° C. (which isrelatively low in comparison to solid-state synthesis routes) can leadto formation of the final composition with low grain-sizes (e.g., withinthe nano dimension, such as 10 nm to 100 nm). Powder particles of thecomposition achieved in this way can be spray-coated by methods referredto above to achieve the final coating with fine-grained microstructure(e.g., 2 to 10 m) which can be retained during heating cycles owing tothe inherent sinter resistance of these compositions.

FIG. 2 is a schematic cross-sectional view of a gas turbine engine inaccordance with an exemplary embodiment of the present disclosure. Moreparticularly, for the embodiment of FIG. 2 , the gas turbine engine is ahigh-bypass turbofan engine 10, referred to herein as “turbofan engine10.” As shown in FIG. 2 , the turbofan engine 10 defines an axialdirection A (extending parallel to a longitudinal axis 12 provided forreference) and a radial direction R. In general, the turbofan engine 10includes a fan section 14 and a core turbine engine 16 disposeddownstream from the fan section 14. Although described below withreference to a turbofan engine 10, the present disclosure is applicableto turbomachinery in general, including turbojet, turboprop andturboshaft gas turbine engines, including industrial and marine gasturbine engines and auxiliary power units. It is also applicable toother high temperature applications that contain water vapor in the gasphase, such as those arising from combustion of hydrocarbon fuels.

The exemplary core turbine engine 16 depicted generally includes asubstantially tubular outer casing 18 that defines an annular inlet 20.The outer casing 18 encases, in serial flow relationship, a compressorsection including a booster or low pressure (LP) compressor 22 and ahigh pressure (HP) compressor 24; a combustion section 26; a turbinesection including a high pressure (HP) turbine 28 and a low pressure(LP) turbine 30; and a jet exhaust nozzle section 32. A high pressure(HP) shaft or spool 34 drivingly connects the HP turbine 28 to the HPcompressor 24. A low pressure (LP) shaft or spool 36 drivingly connectsthe LP turbine 30 to the LP compressor 22.

For the embodiment depicted, the fan section 14 includes a variablepitch fan 38 having a plurality of fan blades 40 coupled to a disk 42 ina spaced apart manner. As depicted, the fan blades 40 extend outwardlyfrom disk 42 generally along the radial direction R. Each fan blade 40is rotatable relative to the disk 42 about a pitch axis P by virtue ofthe fan blades 40 being operatively coupled to a suitable actuationmember 44 configured to collectively vary the pitch of the fan blades 40in unison. The fan blades 40, disk 42, and actuation member 44 aretogether rotatable about the longitudinal axis 12 by LP spool 36 acrossan optional power gear box 46. The power gear box 46 includes aplurality of gears for stepping down the rotational speed of the LPspool 36 to a more efficient rotational fan speed.

Referring still to the exemplary embodiment of FIG. 2 , the disk 42 iscovered by rotatable front nacelle 48 aerodynamically contoured topromote an airflow through the plurality of fan blades 40. Additionally,the exemplary fan section 14 includes an annular fan casing or outernacelle 50 that circumferentially surrounds the fan 38 and/or at least aportion of the core turbine engine 16. It should be appreciated that thenacelle 50 may be configured to be supported relative to the coreturbine engine 16 by a plurality of circumferentially-spaced outletguide vanes 52. Moreover, a downstream section 54 of the nacelle 50 mayextend over an outer portion of the core turbine engine 16 so as todefine a bypass airflow passage 56 therebetween.

During operation of the turbofan engine 10, a volume of air 58 entersthe turbofan engine 10 through an associated inlet 60 of the nacelle 50and/or fan section 14. As the volume of air 58 passes across the fanblades 40, a first portion of the air 58 as indicated by arrows 62 isdirected or routed into the bypass airflow passage 56 and a secondportion of the air 58 as indicated by arrow 64 is directed or routedinto the LP compressor 22. The ratio between the first portion of air 62and the second portion of air 64 is commonly known as a bypass ratio.The pressure of the second portion of air 64 is then increased as it isrouted through the high pressure (HP) compressor 24 and into thecombustion section 26, where it is mixed with fuel and burned to providecombustion gases 66.

The combustion gases 66 are routed through the HP turbine 28 where aportion of thermal and/or kinetic energy from the combustion gases 66 isextracted via sequential stages of HP turbine stator vanes 68 that arecoupled to the outer casing 18 and HP turbine rotor blades 70 that arecoupled to the HP shaft or spool 34, thus causing the HP shaft or spool34 to rotate, thereby supporting operation of the HP compressor 24. Thecombustion gases 66 are then routed through the LP turbine 30 where asecond portion of thermal and kinetic energy is extracted from thecombustion gases 66 via sequential stages of LP turbine stator vanes 72that are coupled to the outer casing 18 and LP turbine rotor blades 74that are coupled to the LP shaft or spool 36, thus causing the LP shaftor spool 36 to rotate, thereby supporting operation of the LP compressor22 and/or rotation of the fan 38.

The combustion gases 66 are subsequently routed through the jet exhaustnozzle section 32 of the core turbine engine 16 to provide propulsivethrust. Simultaneously, the pressure of the first portion of air 62 issubstantially increased as the first portion of air 62 is routed throughthe bypass airflow passage 56 before it is exhausted from a fan nozzleexhaust section 76 of the turbofan engine 10, also providing propulsivethrust. The HP turbine 28, the LP turbine 30, and the jet exhaust nozzlesection 32 at least partially define a hot gas path 78 for routing thecombustion gases 66 through the core turbine engine 16.

Further aspects of the disclosure are provided by the subject matter ofthe following clauses:

1. A composition comprising: a rare earth-doped zirconium/hafnium oxidehaving a defect-fluorite structure or a pyrochlore structure, whereinthe rare earth-doped zirconium/hafnium oxide has a formula: (Ln¹ _(a)Ln²_(a)Ln³ _(a)Ln⁴ _(a)Ln⁵ _(b))₂M₂O₇ where each of Ln¹, Ln², Ln³, Ln⁴, andLn⁵ is a different rare earth element such that Ln¹ and M have a firstatomic radius ratio that is 1.35 to 1.45, Ln² and M have a second atomicradius ratio that is 1.35 to 1.45, Ln³ and M have a third atomic radiusratio that is 1.46 to 1.78, and Ln⁴ and M have a fourth radius ratiothat is 1.46 to 1.78; a is 0.2 or 0.25; b is 0.2 when a is 0.2, and b is0 when a is 0.25; and M is Zr, Hf, or a mixture thereof.

2. The composition of any preceding clause, where a is 0.2 such that therare earth-doped zirconium/hafnium oxide has a formula: (Ln¹ _(0.2)Ln²_(0.2)Ln³ _(0.2)Ln⁴ _(0.2)Ln⁵ _(0.2))₂M₂O₇ where each of Ln¹, Ln², Ln³,Ln⁴, and Ln⁵ is a different rare earth element such that Ln¹ and M havea first atomic radius ratio that is 1.35 to 1.45, Ln² and M have asecond atomic radius ratio that is 1.35 to 1.45, Ln³ and M have a thirdatomic radius ratio that is 1.46 to 1.78, and Ln⁴ and M have a fourthradius ratio that is 1.46 to 1.78; and M is Zr, Hf, or a mixturethereof.

3. The composition of any preceding clause, wherein Ln⁵ and M have asecond atomic radius ratio that is either 1.35 to 1.45 or 1.46 to 1.78.

4. The composition of any preceding clause, where a is 0.25 and b is 0such that the rare earth-doped zirconium/hafnium oxide has a formula:(Ln¹ _(0.25)Ln² _(0.25)Ln³ _(0.25)Ln⁴ _(0.25))₂M₂O₇ where each of Ln¹,Ln², Ln³, and Ln⁴ is a different rare earth element such that Ln¹ and Mhave a first atomic radius ratio that is 1.35 to 1.45, Ln² and M have asecond atomic radius ratio that is 1.35 to 1.45, Ln³ and M have a thirdatomic radius ratio that is 1.46 to 1.78, and Ln⁴ and M have a fourthradius ratio that is 1.46 to 1.78; and M is Zr, Hf, or a mixturethereof.

5. The composition of any preceding clause, where M is 50 atomic % to100 atomic % of Zr.

6. The composition of any preceding clause, where M is 95 atomic % to100 atomic % of Zr.

7. The composition of any preceding clause, where M consists of Zr.

8. The composition of any preceding clause, wherein each of Ln¹ and Ln²is a different rare earth element selected from the group consisting ofTb, Dy, Y, Ho, Er, Tm, Yb, and Lu.

9. The composition of any preceding clause, wherein each of Ln³ and Ln⁴is a different rare earth element selected from the group consisting ofLa, Ce, Pr, Nd, Pm, Sm, Eu, and Gd.

10. The composition of any preceding clause, wherein the composition hasa thermal conductivity of 0.5 W/m-K to 1.5 W/m-K at 1000° C. in a95-100% dense puck, as measured via a laser flash method according toASTM E1461-13.

11. The composition of any preceding clause, wherein the composition isselected from the group consisting of:(Nd_(0.2)Eu_(0.2)Y_(0.2)Dy_(0.2)Lu_(0.2))₂Zr₂O₇;(Nd_(0.2)Eu_(0.2)Tb_(0.2)Dy_(0.2)Lu_(0.2))₂Zr₂O₇;(Sm_(0.2)Eu_(0.2)Gd_(0.2)Dy_(0.2)Lu_(0.2))₂Zr₂O₇;(Sm_(0.2)Eu_(0.2)Y_(0.2)Dy_(0.2)Lu_(0.2))₂Zr₂O₇;(Nd_(0.2)Eu_(0.2)La_(0.2)Dy_(0.2)Lu_(0.2))₂Zr₂O₇;(Nd_(0.2)Eu_(0.2)Ho_(0.2)Dy_(0.2)Lu_(0.2))₂Zr₂O₇;(Nd_(0.2)Eu_(0.2)Y_(0.2)Dy_(0.2)Er_(0.2))₂Zr₂O₇;(Nd_(0.2)Eu_(0.2)Ho_(0.2)Dy_(0.2)Er_(0.2))₂Zr₂O₇;(Sm_(0.2)Eu_(0.2)Ho_(0.2)Dy_(0.2)Lu_(0.2))₂Zr₂O₇;(Nd_(0.25)Eu_(0.25)Ho_(0.25)Dy_(0.25))₂Zr₂O₇;(Nd_(0.25)Eu_(0.25)Y_(0.25)Dy_(0.25))₂Zr₂O₇;(Sm_(0.25)Eu_(0.25)Ho_(0.25)Dy_(0.25))₂Zr₂O₇; and mixtures thereof.

12. A coated component, comprising: a substrate having a surface; athermal barrier coating on the surface, wherein the thermal barriercoating includes a layer comprising the composition of any precedingclause.

13. A coated component, comprising: a substrate having a surface; athermal barrier coating on the surface, wherein the thermal barriercoating includes a layer comprising a rare earth-doped zirconium/hafniumoxide having a defect-fluorite structure or a pyrochlore structure,wherein the layer has a thermal conductivity of 0.5 W/m-K to 1.5 W/m-Kat 1000° C. in a 95-100% dense puck, as measured via a laser flashmethod according to ASTM E1461-13.

14. The coated component of any preceding clause, wherein the layer hasan indentation fracture toughness of 2 MPa-m^(0.5) to 3 MPa-m^(0.5) in a95-100% dense puck.

15. The coated component of any preceding clause, wherein the rareearth-doped zirconium/hafnium oxide includes 4 or 5 different rare earthelements that are each present in a substantially equal atomicpercentage.

16. The coated component of any preceding clause, wherein the layerincludes a single phase of the rare earth-doped zirconium/hafnium oxidein a defect-fluorite structure.

17. The coated component of any preceding clause, wherein the layerincludes a single phase of the rare earth-doped zirconium/hafnium oxidein a pyrochlore structure.

18. The coated component of any preceding clause, wherein the rareearth-doped zirconium/hafnium oxide having a defect-fluorite structureor a pyrochlore structure has a formula: (Ln¹ _(a)Ln² _(a)Ln³ _(a)Ln⁴_(a)Ln⁵ _(b))₂M₂O₇ where each of Ln¹, Ln², Ln³, Ln⁴, and Ln⁵ is adifferent rare earth element such that Ln¹ and M have a first atomicradius ratio that is 1.35 to 1.45, Ln² and M have a second atomic radiusratio that is 1.35 to 1.45, Ln³ and M have a third atomic radius ratiothat is 1.46 to 1.78, and Ln⁴ and M have a fourth radius ratio that is1.46 to 1.78; a is 0.2 or 0.25; b is 0.2 when a is 0.2, and b is 0 whena is 0.25; M is Zr, Hf, or a mixture thereof.

19. The coated component of any preceding clause, where M is 95 atomic %to 100 atomic % of Zr.

20. A method of forming a rare earth-doped zirconium/hafnium oxide, themethod comprising: combining 4 or 5 different rare earthzirconium/hafnium oxides to form a rare earth-doped zirconium/hafniumoxide having a defect-fluorite structure or a pyrochlore structure,wherein a first rare earth oxide includes a first rare earth elementhaving a first atomic radius ratio to Zr that is 1.35 to 1.45, a secondrare earth includes a second rare earth element having a second atomicradius ratio to Zr that is 1.35 to 1.45, a third rare earth oxideincludes a third rare earth element having a first atomic radius ratioto Zr that is 1.46 to 1.78, and a fourth rare earth oxide includes afourth rare earth element having a fourth atomic radius ratio to Zr thatis 1.46 to 1.78, and wherein each of the different rare earthzirconium/hafnium oxides are present in substantially equal atomicamounts of their respective rare earth elements.

This written description uses exemplary embodiments to disclose thedisclosure, including the best mode, and also to enable any personskilled in the art to practice the disclosure, including making andusing any devices or systems and performing any incorporated methods.The patentable scope of the disclosure is defined by the claims, and mayinclude other examples that occur to those skilled in the art. Suchother examples are intended to be within the scope of the claims if theyinclude structural elements that do not differ from the literal languageof the claims, or if they include equivalent structural elements withinsubstantial differences from the literal languages of the claims.

What is claimed is:
 1. A composition comprising: a rare earth-dopedzirconium/hafnium oxide having a defect-fluorite structure or apyrochlore structure, wherein the rare earth-doped zirconium/hafniumoxide has a formula:(Ln¹ _(a)Ln² _(a)Ln³ _(a)Ln⁴ _(a)Ln⁵ _(b))₂M₂O₇ where: each of Ln¹, Ln²,Ln³, Ln⁴, and Ln⁵ is a different rare earth element such that Ln¹ and Mhave a first atomic radius ratio that is 1.35 to 1.45, Ln² and M have asecond atomic radius ratio that is 1.35 to 1.45, Ln³ and M have a thirdatomic radius ratio that is 1.46 to 1.78, and Ln⁴ and M have a fourthradius ratio that is 1.46 to 1.78; a is 0.2 or 0.25; b is 0.2 when a is0.2, and b is 0 when a is 0.25; and M is Zr, Hf, or a mixture thereof.2. The composition of claim 1, where a is 0.2 such that the rareearth-doped zirconium/hafnium oxide has a formula:(Ln¹ _(0.2)Ln² _(0.2)Ln³ _(0.2)Ln⁴ _(0.2)Ln⁵ _(0.2))₂M₂O₇ where: each ofLn¹, Ln², Ln³, Ln⁴, and Ln⁵ is a different rare earth element such thatLn¹ and M have a first atomic radius ratio that is 1.35 to 1.45, Ln² andM have a second atomic radius ratio that is 1.35 to 1.45, Ln³ and M havea third atomic radius ratio that is 1.46 to 1.78, and Ln⁴ and M have afourth radius ratio that is 1.46 to 1.78; and M is Zr, Hf, or a mixturethereof.
 3. The composition of claim 2, wherein Ln⁵ and M have a secondatomic radius ratio that is either 1.35 to 1.45 or 1.46 to 1.78.
 4. Thecomposition of claim 1, where a is 0.25 and b is 0 such that the rareearth-doped zirconium/hafnium oxide has a formula:(Ln_(0.25)Ln² _(0.25)Ln³ _(0.25)Ln⁴ _(0.25))₂M₂O₇ where: each of Ln¹,Ln², Ln³, and Ln⁴ is a different rare earth element such that Ln¹ and Mhave a first atomic radius ratio that is 1.35 to 1.45, Ln² and M have asecond atomic radius ratio that is 1.35 to 1.45, Ln³ and M have a thirdatomic radius ratio that is 1.46 to 1.78, and Ln⁴ and M have a fourthradius ratio that is 1.46 to 1.78; and M is Zr, Hf, or a mixturethereof.
 5. The composition of claim 1, where M is 50 atomic % to 100atomic % of Zr.
 6. The composition of claim 1, where M is 95 atomic % to100 atomic % of Zr.
 7. The composition of claim 1, where M consists ofZr.
 8. The composition of claim 1, wherein each of Ln¹ and Ln² is adifferent rare earth element selected from the group consisting of Tb,Dy, Y, Ho, Er, Tm, Yb, and Lu.
 9. The composition of claim 1, whereineach of Ln³ and Ln⁴ is a different rare earth element selected from thegroup consisting of La, Ce, Pr, Nd, Pm, Sm, Eu, and Gd.
 10. Thecomposition of claim 1, wherein the composition has a thermalconductivity of 0.5 W/m-K to 1.5 W/m-K at 1000° C. in a 95-100% densepuck, as measured via a laser flash method according to ASTM E1461-13.11. The composition of claim 1, wherein the composition is selected fromthe group consisting of:(Nd_(0.2)Eu_(0.2)Y_(0.2)Dy_(0.2)Lu_(0.2))₂Zr₂O₇;(Nd_(0.2)Eu_(0.2)Tb_(0.2)Dy_(0.2)Lu_(0.2))₂Zr₂O₇;(Sm_(0.2)Eu_(0.2)Gd_(0.2)Dy_(0.2)Lu_(0.2))₂Zr₂O₇;(Sm_(0.2)Eu_(0.2)Y_(0.2)Dy_(0.2)Lu_(0.2))₂Zr₂O₇;(Nd_(0.2)Eu_(0.2)La_(0.2)Dy_(0.2)Lu_(0.2))₂Zr₂O₇;(Nd_(0.2)Eu_(0.2)Ho_(0.2)Dy_(0.2)Lu_(0.2))₂Zr₂O₇;(Nd_(0.2)Eu_(0.2)Y_(0.2)Dy_(0.2)Er_(0.2))₂Zr₂O₇;(Nd_(0.2)Eu_(0.2)Ho_(0.2)Dy_(0.2)Er_(0.2))₂Zr₂O₇;(Sm_(0.2)Eu_(0.2)Ho_(0.2)Dy_(0.2)Lu_(0.2))₂Zr₂O₇;(Nd_(0.25)Eu_(0.25)Ho_(0.25)Dy_(0.25))₂Zr₂O₇;(Nd_(0.25)Eu_(0.25)Y_(0.25)Dy_(0.25))₂Zr₂O₇;(Sm_(0.25)Eu_(0.25)Ho_(0.25)Dy_(0.25))₂Zr₂O₇; and mixtures thereof. 12.A coated component, comprising: a substrate having a surface; and athermal barrier coating on the surface, wherein the thermal barriercoating includes a layer comprising the composition of claim
 1. 13. Acoated component, comprising: a substrate having a surface; and athermal barrier coating on the surface, wherein the thermal barriercoating includes a layer comprising a rare earth-doped zirconium/hafniumoxide having a defect-fluorite structure or a pyrochlore structure,wherein the layer has a thermal conductivity of 0.5 W/m-K to 1.5 W/m-Kat 1000° C. in a 95-100% dense puck, as measured via a laser flashmethod according to ASTM E1461-13.
 14. The coated component of claim 13,wherein the layer has an indentation fracture toughness of 2 MPa-m^(0.5)to 3 MPa-m^(0.5) in a 95-100% dense puck.
 15. The coated component ofclaim 13, wherein the rare earth-doped zirconium/hafnium oxide includes4 or 5 different rare earth elements that are each present in asubstantially equal atomic percentage.
 16. The coated component of claim13, wherein the layer includes a single phase of the rare earth-dopedzirconium/hafnium oxide in a defect-fluorite structure.
 17. The coatedcomponent of claim 13, wherein the layer includes a single phase of therare earth-doped zirconium/hafnium oxide in a pyrochlore structure. 18.The coated component of claim 13, wherein the rare earth-dopedzirconium/hafnium oxide having a defect-fluorite structure or apyrochlore structure has a formula:(Ln¹ _(a)Ln² _(a)Ln³ _(a)Ln⁴ _(a)Ln⁵ _(b))₂M₂O₇ where each of Ln¹, Ln²,Ln³, Ln⁴, and Ln⁵ is a different rare earth element such that Ln¹ and Mhave a first atomic radius ratio that is 1.35 to 1.45, Ln² and M have asecond atomic radius ratio that is 1.35 to 1.45, Ln³ and M have a thirdatomic radius ratio that is 1.46 to 1.78, and Ln⁴ and M have a fourthradius ratio that is 1.46 to 1.78; a is 0.2 or 0.25; b is 0.2 when a is0.2, and b is 0 when a is 0.25; and M is Zr, Hf, or a mixture thereof.19. The coated component of claim 13, where M is 95 atomic % to 100atomic % of Zr.
 20. A method of forming a rare earth-dopedzirconium/hafnium oxide, the method comprising: combining 4 or 5different rare earth zirconium/hafnium oxides to form a rare earth-dopedzirconium/hafnium oxide having a defect-fluorite structure or apyrochlore structure, wherein a first rare earth oxide includes a firstrare earth element having a first atomic radius ratio to Zr that is 1.35to 1.45, a second rare earth includes a second rare earth element havinga second atomic radius ratio to Zr that is 1.35 to 1.45, a third rareearth oxide includes a third rare earth element having a first atomicradius ratio to Zr that is 1.46 to 1.78, and a fourth rare earth oxideincludes a fourth rare earth element having a fourth atomic radius ratioto Zr that is 1.46 to 1.78, and wherein each of the different rare earthzirconium/hafnium oxides are present in substantially equal atomicamounts of their respective rare earth elements.